In the worst case, which is if the applet is contained in a third-party jar, one could construct an instance of the Applet, invoke its init() method and add it to a Frame (or for a JApplet, set its contentPane to be the contentPane of a JFrame).

If the source is available, it should be trivial to refactor the game to be housed in a JPanel which can then be set as the contentPane for either a JApplet or a JFrame, which gives the maximum flexibility and is the preferred development route for any game or other GUI which may be required to be run either as a local application or in a browser window, as an applet.